Problem: Umaima is 3 times as old as Nadia. Sixteen years ago, Umaima was 7 times as old as Nadia. How old is Nadia now?
Answer: We can use the given information to write down two equations that describe the ages of Umaima and Nadia. Let Umaima's current age be $u$ and Nadia's current age be $n$ The information in the first sentence can be expressed in the following equation: $u = 3n$ Sixteen years ago, Umaima was $u - 16$ years old, and Nadia was $n - 16$ years old. The information in the second sentence can be expressed in the following equation: $u - 16 = 7(n - 16)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $n$ , it might be easiest to use our first equation for $u$ and substitute it into our second equation. Our first equation is: $u = 3n$ . Substituting this into our second equation, we get: $3n$ $-$ $16 = 7(n - 16)$ which combines the information about $n$ from both of our original equations. Simplifying the right side of this equation, we get: $3 n - 16 = 7 n - 112$ Solving for $n$ , we get: $4 n = 96.$ $n = 24$.